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# Measure Diameter of a Small Spherical Body Using Vernier Callipers

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## Vernier Callipers

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Vernier calliper was invented by a French Mathematician named Pierre Vernier in 1631. It is an instrument for making very accurate measurements.

Vernier calliper works on the principle that vernier scale uses the alignment of line segments that can be displaced by small amounts for the measurement.

It uses two scales viz: the main scale and the auxiliary scale. The main is similar to the ruler, while the vernier scale slides on the main scale that makes readings to the fraction of a division on the main scale.

### Vernier Calliper Measurement

Vernier callipers are used in the two following areas:

• In scientific laboratories.

• For quality control measurements.

Vernier callipers measure the diameter of small spherical objects, depth, and length very accurately, thatâ€™s why they are called Precision measuring instruments.

### Parts of Vernier Calliper

A vernier calliper has the following parts:

1. Outside Jaws: To measure the external diameter of a small spherical object.

2. Inside Jaws: To measure the internal dimension of a small spherical object.

3. Measuring Depth Probe: For measuring the depth of objects.

4. Main Scale: In cm.

5. Main Scale: in inches.

6. Vernier Scales: In cm.

7. Vernier Scales: In inches.

8. Retainer: To block the movable part.

The formula for the vernier calliper measurement is:

Measurement = MSR + (VSR * L.C.)

The least count of the vernier calliper is:

L.C.Â  measurement = 1 MSD - 1VSD

Objective: To ascertain the diameter of a spherical body.

Apparatus/Materials Required:

• Spherical object viz: a spherical marble piece, or a pendulum bob.

• Vernier Calliper.

• Magnifying glass.

Theory

The smallest distance that can be measured along with the distance is the least count or L.C. L.C.is the difference between one main scale division and one vernier scale division.

The formula for the same is given below:

n (MSD) = (n - 1) VSD

Here,

MSD = Main scale division.

VSD = Vernier scale division.

### Measure Diameter of a Small Spherical Using Vernierâ€™s Callipers

Procedure to measure diameter of a small spherical cylindrical body using vernierâ€™s callipers is as follows:

• Check with the instrument, keep both the jaws closed and make sure that the zero of the main scale and the vernier scale coincide with each other.

• Now, use a magnifying glass to check whether we were able to coincide the two zeroes and then check the number of divisions coinciding with each other.

• Release the movable jaw by opening the screw. Put the cylindrical spherical body inside these jaws but not tightly. Make sure that these jaws lie perpendicular to the body. Slowly and gently tighten the screw to adjust the instrument in the position of the body.

• Note the position of zero of the vernier scale against the main scale ( we wonâ€™t get the perfect coincide). Now, read the reading on the main scale division to the left of the zero marks of the vernier scale (V.S.).

• Find the precise coincidence of the main scale division with the vernier scale division in the vernier window, moving from the left end to the right and then note down number â€˜Mâ€™.

• Multiply the least count of the instrument with the number â€˜Mâ€™. Add the acquired product to the main scale reading noted in step 4. We need to make sure that the product so obtained is to be converted into proper units for addition.

• Now, repeat the steps from 3 to 6, do the measurements along with the different positions of the curved surface of the sphere, and obtain at least three readings in each case.

• Finally, record all the observations in a tabular form and apply the arithmetic mean of the correct readings of the diameter of the body.

### What did you Observe?

We observed the following things:

• Main scale 1 mmÂ  = 0.1 cm.

• Number of vernier scale division (M) = 10.

• If 10 vernier scale divisions are equal to 9 main scale divisions, then:

1 vernier scale division is equal to 0.9 main scale divisions.

• Vernier constantÂ  = 1 MSD - 1 VSDÂ  = 1 - 0.9 = 0.1 main scale divisions

• So, we get the vernier constant as 0.1 MSD = 0.1 mm = 0.01 cm.

So, this was the procedure to measure the diameter of a small spherical. Now, record all the readings in the table given below:

The table form for noting the details of measuring the diameter of a small spherical is:

 S.No. Main Scale Reading (N) No of Coinciding Vernier Division (K) Vernier Scale Reading, V = N * Vc (in cm or mm) The Measured Diameter is Equal to N + V (cm or mm)

Zero error = Â± â€¦â€¦cm.

Mean observed diameter in cm = â€¦â€¦

The formula for the corrected diameter is the difference between the mean observed diameter and the zero error.

Our final result is:

The diameter of the cylinder or the sphere inâ€¦...cm.

Question 1: Write the Advantages of Vernier Callipers.

• Vernier callipers provide precise measurements at large scales.

• It can measure any type of dimension of the component like the measure of length, depth, inner, and the outer diameter of the body.

• Vernier calliper is made up of a stainless steel material so it has long durability.

• Less expensive.

Question 2: State the Disadvantage of the Vernier Calliper.

Answer: A vernier calliper requires good concentration to observe the measured quantity or you can use a magnifying glass to observe the measurement.

Question 3: State the Applications of Vernier Callipers.

Answer: The applications of vernier callipers lie hereunder:

• In educational sectors.

• Physics laboratories.

• Employed in steel industries.

• In aerospace industries.

• For medical purposes.

Question 4: State the Precautions to be Taken While Using Vernier Callipers.

Answer: The following are the ways to use vernier callipers:

• Make sure that the vernier scale slides easily over the main scale. If it doesnâ€™t, you can use grease or a machine oil for its smooth movement.

• Focus on the division mark to avoid the parallax error.

• Carefully screw the vernier calliper without creating any pressure and to avoid damages in the rings/threads of the screw.